MAYOR MARION BARRY has worked long and sensitively through the weekend, to come up with a compromise that could lead to the reopening of Washington's public schools. Though neither the school board nor the teachers' union was pleased yesterday with the language of the mayor's proposal, it offers a reasonable set of conditions for resuming negotiations and -- more important -- for getting things back to normal in the city's classrooms. Acceptance by both parties could mean the immediate resumption of classes.

The mayor's plan is neither pro-board nor prounion. Aware that he is without a clearly defined legal role in this dispute, Mayor Barry has made no attempt to negotiate substantive issues. Instead, his proposal asks the teachers to call off their strike in return for guarantees by the board that there would be no reprisals against striking teaches; and it asks the board to reinstate thoser portions of the expired union contract that guarantee grievance procedures for teachers.

Missing from this are the sections of the teacher-board contract that are in dispute -- having to do with the length of the school day and the school year, the evaluation of teachers and the automatic deduction of union dues from teacher payschecks. The board wants longer hours for teachers -- which, since no salary increases can be negotiated in the contract -- would mean a pay cut for teachers. The teachers would be content just to extend the expired contract, but aer particularly concerned about preserving the dues clause.

Rather than attempt to resolve these issues, Mayor Barry's proposal would establish a three-member fact-finding panel with a representative from each side and one neutral party. This group would recommend its solutions to resolve the issues no later than April 16. Then both sides could act on the recommendations, or the courts could intercede.

Obviously, the mayor's plan does not settle may issues in the dispute. But how much longer are the two sides going to sit around worrying about saving face? Under the terms of the plan, the teachers would lose nothing by returning to work; and the board, which has conceded nothing to the teachers so far, and only reluctantly agreed yesterday to hold its first meeting today since the strike began, would not give up anything. In offering a way out of this impasse -- at least temporarily -- Mayor Barry has rightly acknowledged his responsibility to protect the interests of the city at large, which include keeping the schools open. The board and the teachers should respect this serious concern by accepting the mediation effort.